mlsanityData to 7 Oct 2026

Regularising Inverse Problems with Generative Machine Learning Models

arXiv 2107.11191 ↗First posted 22 Jul 2021eess.IV cs.CV cs.LGcited by 22

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Abstract (arXiv)

Deep neural network approaches to inverse imaging problems have produced impressive results in the last few years. In this paper, we consider the use of generative models in a variational regularisation approach to inverse problems. The considered regularisers penalise images that are far from the range of a generative model that has learned to produce images similar to a training dataset. We name this family textitgenerative regularisers. The success of generative regularisers depends on the quality of the generative model and so we propose a set of desired criteria to assess generative models and guide future research. In our numerical experiments, we evaluate three common generative models, autoencoders, variational autoencoders and generative adversarial networks, against our desired criteria. We also test three different generative regularisers on the inverse problems of deblurring, deconvolution, and tomography. We show that restricting solutions of the inverse problem to lie exactly in the range of a generative model can give good results but that allowing small deviations from the range of the generator produces more consistent results.

Key facts. Cited by 22 papers in the map (data through 7 Oct 2026). Builds on 70 of its 130 references that are in the map. First posted on arXiv 22 Jul 2021.

Builds on

70 of 130 references.

References · 70

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38 more
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 3; 2023: 4; 2024: 4; 2025: 3; 2026: 8.

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  1. 2022A Neural-Network-Based Convex Regularizer for Inverse Problemscited by 40
  2. 2022PatchNR: Learning from Very Few Images by Patch Normalizing Flow Regularizationcited by 22
  3. 2023Manifold Learning by Mixture Models of VAEs for Inverse Problemscited by 16
  4. 2023Steerable Conditional Diffusion for Out-of-Distribution Adaptation in Medical Image Reconstructioncited by 15
  5. 2025Learning Regularization Functionals for Inverse Problems: A Comparative Studycited by 12
  6. 2022Compressed Sensing MRI Reconstruction Regularized by VAEs with Structured Image Covariancecited by 4
  7. 2023Variational Bayes image restoration with compressive autoencoderscited by 4
  8. 2024Iteratively Refined Image Reconstruction with Learned Attentive Regularizerscited by 3
  9. 2026Error Analysis of Bayesian Inverse Problems with Generative Priorscited by 2
  10. 2026Conditional flow matching for physics-constrained inverse problems with finite training datacited by 2
  11. 2024Deep priors for satellite image restoration with accurate uncertaintiescited by 1
  12. 2026Weakly Convex Ridge Regularization for 3D Non-Cartesian MRI Reconstructioncited by 1
10 more
  1. 2026A Stability Benchmark of Generative Regularizers for Inverse Problemscited by 1
  2. 2023Adversarial Generative NMF for Single Channel Source Separationcited by 0
  3. 2024Multibranch Generative Models for Multichannel Imaging with an Application to PET/CT Synergistic Reconstructioncited by 0
  4. 2024Maximum Discrepancy Generative Regularization and Non-Negative Matrix Factorization for Single Channel Source Separationcited by 0
  5. 2025RELD: Regularization by Latent Diffusion Models for Image Restorationcited by 0
  6. 2025Enhancing Obsolescence Forecasting with Deep Generative Data Augmentation: A Semi-Supervised Framework for Low-Data Industrial Applicationscited by 0
  7. 2026Allure of Craquelure: A Variational-Generative Approach to Crack Detection in Paintingscited by 0
  8. 2026A Diffusion-Based Generative Prior Approach to Sparse-view Computed Tomographycited by 0
  9. 2026FlowADMM: Plug-and-play ADMM with Flow-based Renoise-Denoise Priorscited by 0
  10. 2026Diffusion Graph Posterior Sampling for Nonlinear Inverse Problems with Application to Electrical Impedance Tomographycited by 0